Find a polar equation of the conic with the given characteristics and with one focus at the pole. $\begin{array} { c c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \ \text { Parabola } & e = 1 & x = - 4 \end{array}$
A) $r = \frac { 4 } { 1 + \sin \theta }$
B) $r = \frac { 4 } { 1 - \sin \theta }$
C) $r = \frac { 4 } { 1 - \cos \theta }$
D) $r = \frac { 4 } { 1 + \cos \theta }$
E) $r = \frac { 1 } { 1 - 4 \cos \theta }$

Question

Quizplus · Accepted Answer

The polar equation of a conic section with eccentricity $e$ and directrix $x = -d$ (where the focus is at the origin) is given by $r = \frac{ed}{1 - e\cos\theta}$. For a parabola, $e = 1$, and given $x = -4$, $d = 4$. Substituting these values gives $r = \frac{4}{1 - \cos\theta}$, which matches option C.

Find a Polar Equation of the Conic with the Given Conic Eccentricity Directrix Parabola e=1x=−4\begin{array} { c c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \\ \text { Parabola } & e = 1 & x = - 4 \end{array} Conic Parabola ​ Eccentricity e=1​ Directrix x=−4​

Find a Polar Equation of the Conic with the Given $\begin{array} { c c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \\ \text { Parabola } & e = 1 & x = - 4 \end{array}$